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Simplifying (4x)(3x + -3) + (5x + 3) = 180 Remove parenthesis around (4x) 4x(3x + -3) + (5x + 3) = 180 Reorder the terms: 4x(-3 + 3x) + (5x + 3) = 180 (-3 * 4x + 3x * 4x) + (5x + 3) = 180 (-12x + 12x2) + (5x + 3) = 180 Reorder the terms: -12x + 12x2 + (3 + 5x) = 180 Remove parenthesis around (3 + 5x) -12x + 12x2 + 3 + 5x = 180 Reorder the terms: 3 + -12x + 5x + 12x2 = 180 Combine like terms: -12x + 5x = -7x 3 + -7x + 12x2 = 180 Solving 3 + -7x + 12x2 = 180 Solving for variable 'x'. Reorder the terms: 3 + -180 + -7x + 12x2 = 180 + -180 Combine like terms: 3 + -180 = -177 -177 + -7x + 12x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -177 + -7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -14.75 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '14.75' to each side of the equation. -14.75 + -0.5833333333x + 14.75 + x2 = 0 + 14.75 Reorder the terms: -14.75 + 14.75 + -0.5833333333x + x2 = 0 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + -0.5833333333x + x2 = 0 + 14.75 -0.5833333333x + x2 = 0 + 14.75 Combine like terms: 0 + 14.75 = 14.75 -0.5833333333x + x2 = 14.75 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 14.75 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 14.75 + 0.08506944446 Combine like terms: 14.75 + 0.08506944446 = 14.83506944446 0.08506944446 + -0.5833333333x + x2 = 14.83506944446 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 14.83506944446 Calculate the square root of the right side: 3.851632049 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 3.851632049 and -3.851632049.Subproblem 1
x + -0.2916666667 = 3.851632049 Simplifying x + -0.2916666667 = 3.851632049 Reorder the terms: -0.2916666667 + x = 3.851632049 Solving -0.2916666667 + x = 3.851632049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 3.851632049 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 3.851632049 + 0.2916666667 x = 3.851632049 + 0.2916666667 Combine like terms: 3.851632049 + 0.2916666667 = 4.1432987157 x = 4.1432987157 Simplifying x = 4.1432987157Subproblem 2
x + -0.2916666667 = -3.851632049 Simplifying x + -0.2916666667 = -3.851632049 Reorder the terms: -0.2916666667 + x = -3.851632049 Solving -0.2916666667 + x = -3.851632049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -3.851632049 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -3.851632049 + 0.2916666667 x = -3.851632049 + 0.2916666667 Combine like terms: -3.851632049 + 0.2916666667 = -3.5599653823 x = -3.5599653823 Simplifying x = -3.5599653823Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.1432987157, -3.5599653823}
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